University:
California State University, Northridge
Course:
MATH 320 | Foundations of Higher Mathematics
Academic year:

2024
Views:

89

Pages:

7
Author:

oretsquareeeup

§ 12.7 Dividing Polynomials Dividing Polynomials Dividing a polynomial by a monomial Divide each term of the polynomial separately by the monomial. Example − 12a 3 + 36a − 15 − 12a 3 36a 15 = + − 3a 3a 3a 3a 5 2 = −4a + 12 − a 55 Dividing Polynomials Dividing a polynomial by a polynomial other than a monomial uses a “long division” technique that is similar to the process known as long division in dividing two numbers, which is reviewed on the next slide. 56 Dividing Polynomials 168 43 7256 43 295 258 37 6 344 32 Divide 43 into 72. Multiply 1 times 43. Subtract 43 from 72. Bring down 5. Divide 43 into 295. Multiply 6 times 43. Subtract 258 from 295. Bring down 6. Divide 43 into 376. Multiply 8 times 43. Subtract 344 from 376. Nothing to bring down. We then write our result as 32 168 . 43 57 Dividing Polynomials As you can see from the previous example, there is a pattern in the long division technique. Divide Multiply Subtract Bring down Then repeat these steps until you can’t bring down or divide any longer. We will incorporate this same repeated technique with dividing polynomials. 58 Dividing Polynomials 4x − 5 2 7 x + 3 28 x − 23 x − 15 2 28 x + 12 x − 35 x − 15 − 35 x − 15 Divide 7x into 28x2. Multiply 4x times 7x+3. Subtract 28x2 + 12x from 28x2 – 23x. Bring down – 15. Divide 7x into –35x. Multiply – 5 times 7x+3. Subtract –35x–15 from –35x–15. Nothing to bring down. So our answer is 4x – 5. 59 Dividing Polynomials 2 x − 10 2 2 x + 7 4x − 6 x + 8 2 4 x + 14 x −20x + 8 −20x − 70 78 Divide 2x into 4x2. Multiply 2x times 2x+7. Subtract 4x2 + 14x from 4x2 – 6x. Bring down 8. Divide 2x into –20x. Multiply -10 times 2x+7. Subtract –20x–70 from –20x+8. Nothing to bring down. We write our final answer as 2 x − 10 + 78 ( 2 x + 7) 60